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Physical Review A

Inverse operators in Fock space studied via a coherent-state approach

Fan Hong‐Yi

Published May 1, 1993• 29 citations
Publisher

Abstract

The Fock representation of the inverse of harmonic-oscillator creation and annihilation operators [see, e.g., C. L. Mehta, Anil K. Roy, and G. M. Saxena, Phys. Rev. A 46, 1565 (1992)] are naturally derived via a coherent-state approach. The completeness relation of Fock space is reexpressed by the inverse operators. Applications of the inverse operators in studying the phase operators and in normally ordering some operators are given.

DOI
10.1103/physreva.47.4521

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The Fock representation of the inverse of harmonic-oscillator creation and annihilation operators [see, e.g., C. L. Mehta, Anil K. Roy, and G. M. Saxena, Phys. Rev. A 46, 1565 (1992)] are naturally derived via a coherent-state approach. The completeness relation of Fock space is reexpressed by the inverse operators. Applications of the inverse operators in studying the phase operators and in normally ordering some operators are given.
Operator algebra techniques are employed to derive the quantum evolution operator for the harmonic oscillator. The derivation begins with the construction of the annihilation and creation operators and the determination of the wave function for the coherent state as well as its time-dependent evolution, and ends with the transformation of the propagator in a mixed position-coherent-state representation to the desired one in configuration space. Throughout the entire procedure, besides elementary operator manipulations, it is only necessary to solve linear differential equations and to calculate Gaussian integrals.